Paper 2019/939

Homomorphic Encryption Standard

Martin Albrecht, Melissa Chase, Hao Chen, Jintai Ding, Shafi Goldwasser, Sergey Gorbunov, Shai Halevi, Jeffrey Hoffstein, Kim Laine, Kristin Lauter, Satya Lokam, Daniele Micciancio, Dustin Moody, Travis Morrison, Amit Sahai, and Vinod Vaikuntanathan


Homomorphic Encryption is a breakthrough technology which can enable private cloud storage and computation solutions, and many applications have been described in the literature in the last few years. But before Homomorphic Encryption can be adopted in medical, health, and financial sectors to protect data and patient and consumer privacy, it will have to be standardized, most likely by multiple standardization bodies and government agencies. An important part of standardization is broad agreement on security levels for varying parameter sets. Although extensive research and benchmarking has been done in the research community to establish the foundations for this effort, it is hard to find all the information in one place, along with concrete parameter recommendations for applications and deployment. This document is the first Homomorphic Encryption Standard (HES) approved by the community in 2018. It captures the collective knowledge on the state of security of these schemes, specifies the schemes, and recommends a wide selection of parameters to be used for homomorphic encryption at various security levels. We describe known attacks and their estimated running times in order to make these security parameter recommendations.

Available format(s)
Publication info
Preprint. MINOR revision.
Homomorphic EncryptionStandardsecurity levelsattacks
Contact author(s)
klauter @ microsoft com
2019-08-18: received
Short URL
Creative Commons Attribution


      author = {Martin Albrecht and Melissa Chase and Hao Chen and Jintai Ding and Shafi Goldwasser and Sergey Gorbunov and Shai Halevi and Jeffrey Hoffstein and Kim Laine and Kristin Lauter and Satya Lokam and Daniele Micciancio and Dustin Moody and Travis Morrison and Amit Sahai and Vinod Vaikuntanathan},
      title = {Homomorphic Encryption Standard},
      howpublished = {Cryptology ePrint Archive, Paper 2019/939},
      year = {2019},
      note = {\url{}},
      url = {}
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